From 1b93a0d16e2373a8b1fffcf65e6860c3e6c48772 Mon Sep 17 00:00:00 2001
From: ZUO Zhihua <zuo.zhihua@qq.com>
Date: Fri, 2 Aug 2024 21:56:17 +0800
Subject: [PATCH] remove duplicate example_real_transform

---
 example/real-forward-transform.f90 | 51 ------------------------------
 1 file changed, 51 deletions(-)
 delete mode 100644 example/real-forward-transform.f90

diff --git a/example/real-forward-transform.f90 b/example/real-forward-transform.f90
deleted file mode 100644
index 8e0d902..0000000
--- a/example/real-forward-transform.f90
+++ /dev/null
@@ -1,51 +0,0 @@
-program forward_transform_of_real_function
-  !! This program invokes fftpack's rrft function to compute the forward transform of a real function
-  !! and constructs the resulting complex Fourier coefficients by (re)organizing and normalizing the
-  !! rfft result according to array element layout described at [1].  The program also demonstrates
-  !! the inverse transform of the raw rrft result to recover the original function.
-  !!
-  !! [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.fftpack.rfft.html#scipy.fftpack.rfft
-  use fftpack, only: rfft, irfft
-  implicit none
-  integer j, k
-  integer, parameter :: N = 8
-  double precision, parameter :: two_pi = 2.D0*acos(-1.D0), tolerance = 1.0D-06, f_avg = 3.D0, zero=0.D0
-  double precision, parameter :: x(0:N-1) = [(two_pi*dble(j)/dble(N), j=0,N-1)]
-  double precision, parameter :: f(0:N-1) = f_avg + cos(x)
-    !! sample f(x) = 3 + cos(x) uniformly on [0,2*pi)
-    !!             = 3 + (exp(i*x) - exp(-i*x))/2  
-    !! which yields the Fourier coefficients
-    !!                { 3, k = 0
-    !!       f_hat =  { 1/2, k = 1
-    !!                { 0, otherwise
-  double precision, dimension(0:N-1) :: f_round_trip, rfft_f
-  integer, parameter :: rk = kind(two_pi)
-  complex(rk) f_hat(0:N/2)
-  character(len=*), parameter :: real_format = "(a,*(g10.4,:,1x))" !! space-separated values
-  character(len=*), parameter :: complex_format= "(a,*('(',g10.4,',',g10.4,')',:,1x)))" !! space-separated complex values
-
-  call assert(mod(N,2)==0, "the algorithm below requires even N")
-
-  rfft_f(:) = rfft(f)/dble(N)
-  f_hat(:) = [ &
-    cmplx(rfft_f(0),zero), &
-    [( cmplx(rfft_f(k),rfft_f(k+1)),  k=lbound(rfft_f,1)+1,ubound(rfft_f,1)-1,2)], &
-    cmplx(zero,rfft_f(N-1)) &
-  ]
-  f_round_trip(:) = irfft(rfft_f)
-
-  print real_format, "f = ", f
-  print complex_format, "f_hat = ", f_hat
-  print real_format, "f_round_trip = ",f_round_trip
-
-  call assert(all(abs(f_round_trip - f) < tolerance), "inverse of forward FFT must yield the original function")
-
-contains
-
-  pure subroutine assert(assertion, description)
-    logical, intent(in) :: assertion
-    character(len=*), intent(in) :: description
-    if (.not. assertion) error stop description
-  end subroutine
-
-end program